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(a) Determine a state variable matrix differential equation for the circuit of Figure 4 (a) where the input is 11 and the output is p. Let x,-p, r,-q Cart 2 Cart 1 M2 1 M11-1 te b2 Figure 4 (a)...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
(11) [CH 2] Design a circuit that takes input signals p, q and r and outputs a 1 if, and only if,...
(11) [CH 2] Design a circuit that takes input signals p, q and r and outputs a 1 if, and only if, all three of p, q and r have the same value. (multi input gates are permitted)
(11) [CH 2] Design a circuit that takes input signals p, q and r and outputs a 1 if, and only if, all three of p, q and r have the same value. (multi input gates are permitted)
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the s...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
Problem 4: The following figure shows a biplolar op-amp circuit, the input differential pair Q,-Q, is...
Problem 4: The following figure shows a biplolar op-amp circuit, the input differential pair Q,-Q, is loaded in a current mirror formed by Q2-Q. The second stage is formed by the current-source-loaded common-emitter transistor Q. Unlike the CMOS circuit, here there is an output stage formed by the emitter follower Q. The function of capacitor Cc will be explained later in feedback chapter. All transistors have B=100, VBE = 0.7V, and r = 0. (a) For inputs grounded and output...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t)...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t) and output y(t) Function Generator R, v, (r) y1) Figure 2: RC circuit. (a) (1 point) Sketch the circuit in the phasor domain by replacing the capacitor with its impedance represen- (b) (3 points) Using circuit analysis techniques, show that the frequency response function is Specify the DC gain, K, and the time constant, T, in terms of the parameters R, R, and C...
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
Let Ax=b be a matrix equation where A is given by 11 -2 3 2 1...
Let Ax=b be a matrix equation where A is given by 11 -2 3 2 1 and b by 3 1 2 1) Show that the equation is inconsistent. (15 points) 2) Find the least squares solution x"hat" of the equation and compute the error. (15 points)
Theorem. Consider the quadratic form Q(x) = Ar where A is anxn symmetric matrix and A,...
Theorem. Consider the quadratic form Q(x) = Ar where A is anxn symmetric matrix and A, and denote the largest and smallest eigenvalues of A, respectively. Then max Q(x) = 2 = max Q() = 1 and Q0.) = 1, where is any unit eige vector corre sponding to ii) in (r) and QU.) where is any unit eigen vector corresponding to do 1. - Find max Q(x) and min Q(x). 1) Q(1) = 3x + 43273 +673 ii) Q(z)...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autoc...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
(11) [CH 2] Design a circuit that takes input signals p, q and r and outputs a 1 if, and only if, all three of p, q and r have the same value. (multi input gates are permitted)
(11) [CH 2] Design a circuit that takes input signals p, q and r and outputs a 1 if, and only if, all three of p, q and r have the same value. (multi input gates are permitted)
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
Problem 4: The following figure shows a biplolar op-amp circuit, the input differential pair Q,-Q, is loaded in a current mirror formed by Q2-Q. The second stage is formed by the current-source-loaded common-emitter transistor Q. Unlike the CMOS circuit, here there is an output stage formed by the emitter follower Q. The function of capacitor Cc will be explained later in feedback chapter. All transistors have B=100, VBE = 0.7V, and r = 0. (a) For inputs grounded and output...
Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t) and output y(t) Function Generator R, v, (r) y1) Figure 2: RC circuit. (a) (1 point) Sketch the circuit in the phasor domain by replacing the capacitor with its impedance represen- (b) (3 points) Using circuit analysis techniques, show that the frequency response function is Specify the DC gain, K, and the time constant, T, in terms of the parameters R, R, and C...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
Let Ax=b be a matrix equation where A is given by 11 -2 3 2 1 and b by 3 1 2 1) Show that the equation is inconsistent. (15 points) 2) Find the least squares solution x"hat" of the equation and compute the error. (15 points)
Theorem. Consider the quadratic form Q(x) = Ar where A is anxn symmetric matrix and A, and denote the largest and smallest eigenvalues of A, respectively. Then max Q(x) = 2 = max Q() = 1 and Q0.) = 1, where is any unit eige vector corre sponding to ii) in (r) and QU.) where is any unit eigen vector corresponding to do 1. - Find max Q(x) and min Q(x). 1) Q(1) = 3x + 43273 +673 ii) Q(z)...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
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